Problem: Divide the following complex numbers: $\dfrac{14 e^{3\pi i / 4}}{7 e^{2\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $14 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius 14. The second number ( $7 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius 7. The radius of the result will be $\frac{14}{7}$ , which is 2. The angle of the result is $\frac{3}{4}\pi - \frac{2}{3}\pi = \frac{1}{12}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{1}{12}\pi$.